Fall 2023
Monday 4.15  5.15 pm
Room 2147
Scheduled virtual talks will be held on Zoom, Monday 4:155:15 pm.
A link to a Zoom classroom will appear here!!
Schedule

September 11
Yier Lin
University of ChicagoMultipoint Lyapunov Exponents of the Stochastic Heat Equation
Abstract: We study the Stochastic Heat Equation with multiplicative spacetime white noise. Extensive research has already been conducted on the onepoint Lyapunov exponents of this equation. In this talk, I will present how we can compute the multipoint Lyapunov exponents by leveraging a combination of integrability and probability. As a byproduct, we also solve a quadratic optimization problem.

September 18
Lingfu Zhang
UC BerkeleyGeodesics in LastPassage Percolation under Large Deviations
Abstract: In KPZ universality, an important family of models arises from 2D lastpassage percolation (LPP): in a 2D i.i.d. random field, one considers the geodesic connecting two vertices, which is defined as the upright path maximizing its weight, i.e., the sum/integral of the random field along it. A characteristic KPZ behavior is the 2/3 geodesic fluctuation exponent, which has been proven for some LPPs with exactly solvable structures. A topic of much recent interest is such models under upper and lowertail large deviations, i.e., when the geodesic weight is atypically large or small. In prior works, it was established that the geodesic exponent changes to 1/2 (more localized) and 1 (delocalized) respectively. In this talk, I will describe a further refined picture: the geodesic converges to a Brownian bridge under the upper tail, and a uniformly chosen function from a oneparameter family under the lower tail. I will also discuss the proofs, using a combination of algebraic, geometric, and probabilistic arguments.
This is based on two forthcoming works, one joint with Shirshendu Ganguly and Milind Hegde, and the other with Shirshendu Ganguly.

September 25
Amol Aggarwal
Columbia UniversityA Characterization for the Airy Line Ensemble
Abstract: The Airy line ensemble is a universal scaling limit that is believed (and in some cases proven) to govern the fluctuations of many probabilistic systems, such as random surfaces, interacting particle systems, and stochastic interfaces. It is an example of a "Brownian line ensemble," which informally means that it is an infinite, ordered sequence of random continuous curves that look like nonintersecting Brownian motions. In this talk we survey recent results characterizing the Airy line ensemble as the unique Brownian line ensemble whose top curve decays parabolically, and we explain why this result is useful for proving convergence theorems for various discrete stochastic models. This is based on joint work with Jiaoyang Huang.

October 2
Morris Ang
Columbia UniversityCutting LQG by SLE with a mismatched central charge
Abstract: There are many deep and useful theorems relating SchrammLoewner evolution (SLE) and Liouville quantum gravity (LQG) when their parameters are matched, meaning $\kappa \in \{ \gamma^2, 16/\gamma^2\}$. Roughly speaking, the SLE curve cuts the LQG surface into two or more independent LQG surfaces. We extend these theorems to the setting of mismatched parameters: an LQG disk is cut by an SLE curve into two or more LQG surfaces which are conditionally independent given the values along the SLE curve of a certain collection of auxiliary imaginary geometry fields. These fields are sampled independently of the LQG and SLE, and have the property that the central charges of the LQG, SLE and auxiliary fields sum to 26. This central charge condition is natural from the perspective of bosonic string theory. Similar statements hold when the SLE curve is replaced by, e.g., an LQG metric ball or a Brownian motion path. These statements are continuum analogs of certain Markov properties of random planar maps decorated by two or more statistical physics models. This work is joint with Ewain Gwynne.

October 9
Indigenous Peoples' Day

October 16
Ramon von Handel
Princeton 
Octobe 23
Hao Shen
UW Madison 
October 30

November 6
Jacopo Borga
Stanford 
November 13

November 20
Bjoern Bringmann
IAS/Princeton 
November 27

December 4

December 11
Michael Magee
Durham University & IAS